Question

multiplying rational expressions
simplify the product \\(\frac{5}{n+1} \cdot \frac{n+1}{n+3}\\).
\\(\frac{5}{n+3}\\) \\(\frac{5n+5}{n^2+4n+3}\\) \\(\frac{5n+1}{n+3}\\)
\\(\frac{5n+1}{n^2+4n+3}\\)

Explanation:

Step1: Identify Common Factors

In the rational expressions $\frac{5}{n + 1}$ and $\frac{n + 1}{n + 3}$, the term $(n + 1)$ appears in the numerator of the second expression and the denominator of the first.

Step2: Cancel Common Factors

Cancel out the common factor $(n + 1)$ from the numerator and denominator:
$$\frac{5}{\cancel{n + 1}} \cdot \frac{\cancel{n + 1}}{n + 3}$$

Step3: Multiply Remaining Terms

After canceling, we multiply the remaining numerators and denominators:
$$\frac{5 \cdot 1}{1 \cdot (n + 3)} = \frac{5}{n + 3}$$

Answer:

$\frac{5}{n + 3}$ (corresponding to the first option box with $\frac{5}{n + 3}$)